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When determining how many #14 AWG wires can be run in 1/2" Flexible Metallic Conduit (FMC), it is essential to refer to the guidelines established by the National Electrical Code (NEC) for wire fill calculations within conduit.

For #14 AWG wire, each wire requires a certain amount of space inside the conduit. According to NEC guidelines, the maximum fill capacity for conductors in a conduit is based on the overall area of the conduit and the cross-sectional area occupied by the conductors.

In the case of a 1/2" FMC, it typically has a certain internal diameter that permits a specific number of #14 AWG wires to be installed without exceeding the fill limits. The calculations show that 3 #14 AWG wires can fit within the 1/2" FMC while complying with safety standards related to heat dissipation and ease of installation.

This is important not only to maintain operational integrity but also to help prevent overheating and ensure that all conductors can be safely and reliably used in electrical systems. Hence, the correct answer indicates that 3 #14 AWG wires can be safely run within the 1/2" FMC.